Creating a cardboard cut-out OR How do I make my geometry respect my 2d image import?
If you use alpha to give transparency I'm not sure you'll be able to give it thickness properly.
What you need to do is use your image as a background, draw a mesh that will have the exact same shape as your star, extrude, unwrap and give it your image as Image Texture.
Or import the shape as svg, make it a mesh, use X &gt; Limited Dissolve to lighten the topology, and same thing, extrude, unwrap and give it the image as Image Texture. In your case the good news is that you won't need to rework the imported SVG.